Structure Dashboard Gadget is a bit limited where it comes to editing issue fields, due to some incompatibilities between field editors and gadget framework. Because of that, only a handful of fields could be edited from within Structure Gadget (of course, if the user has permissions to edit them and only if those fields are added to the Edit Screen).

The following fields are editable from Structure Gadget:

All other fields, including custom fields, cannot be edited in the Gadget. To edit those fields, open Structure Board or issue page or any other page with the structure.